In the OSTI Collections: Dark Matter and Dark Energy

Recent observations of the universe, combined with Einstein’s theory of general relativity, indicate that most of the universe consists of entities very different from the matter and energy long familiar to us. These previously unknown entities are beginning to be explored on several fronts, many through Department of Energy sponsorship.

Albert Einstein’s theory of relativity describes space and time as observer-dependent aspects of a single absolute entity (spacetime). According to the theory, just as a two-dimensional surface can be curved, four-dimensional spacetime is also curved, with the curvature at different places and times being partly determined by how matter (or equivalently, energy) is distributed within it. Where curvature is lacking, matter will move along straight paths at constant speeds; where spacetime is curved, matter will follow the straightest possible paths along the curves, changing direction and speed as it follows those curved paths. The exact changes described by the theory match the known effects of gravity on the motion of matter. Relativity theory thus represents the mechanism of gravity as the effect of matter curving the spacetime it occupies and then following the straightest possible paths along the curves.

Einstein didn’t simply propose the basic mechanism described above, but worked out a precise equation to relate features of the spacetime curvature to the distribution of matter within spacetime:

The gmn expresses how distances between events in spacetime depend on how the events are separated along each of the four dimensions of space and time. Gmn is a function of gmn that stands for certain features of spacetime curvature determined by the matter distribution, which is itself described by Tmn. (the Greek letter lambda) is a constant, c is the speed of light, and K is another constant that appears in Isaac Newton’s formula for gravity.

To even be plausible, any theory has to conform to real observations. Einstein’s equation passes this test with two well-verified sets of facts. First, it matches the law that every known natural process in any given region of spacetime ends with the same total amount of matter and energy that it starts with, no more and no less—expressed mathematically, the divergenceTmn;n of the matter and energy is zero. Both gmn and the particular features of spacetime curvature described by Gmn constitute geometrical entities whose divergences gmn;n and Gmn;n are themselves always zero for any shape of spacetime whatsoever. So taking the divergences of both sides of Einstein’s equation results in a new, true equation, which means Einstein’s equation automatically passes the first test. Second, for material objects that move past their neighbors very slowly compared to the speed of light and have relatively low internal stresses—the state of most objects within solar systems—Einstein’s equation should reduce to Isaac Newton’s law of gravity, which was already known to accurately predict the motions of such objects. Einstein’s equation does reduce to Newton’s, if the constant is small.

On the other hand, Einstein’s formula differs from Newton’s in how it describes matter and spacetime in a wider range of conditions than that observed in Newton’s time, and fits the newer observations much more accurately. Among these newer observations are precise details of the planet Mercury’s motion around the sun, the focusing of light as it passes near massive objects in space (gravitational lensing), the delay in radar signals passing near the sun, the effect of gravity on the energy of photons rising through a gravitational field, and the changes in orientation of gyroscopes orbiting the earth. These phenomena, plus the many others in which Einstein’s equation reduces to Newton’s, give physicists considerable reason to take its implications seriously.

One implication is that most of what the universe consists of is invisible. Furthermore, it’s apparently like nothing we’ve previously become familiar with.

In fact, the invisible portion consists of two different entities, with two different effects on the universe and things in it. They’ve been named “dark matter” and “dark energy”—the term “dark” simply referring to their invisibility, in contrast to luminous matter such as stars and the other visible matter that we see by its light. Strictly speaking, matter and energy are equivalent (E=mc2), so the terms “dark matter” and “dark energy” incorrectly suggest that the two entities are essentially the same, but they aren’t. More important than the names is the currently mysterious nature of what they refer to. Several different approaches are being taken to solve the mysteries.[References]

The coherence of galaxies and dark matter

The speed and path of an object in spacetime give us information about the curvature and the distribution of matter that shapes it. Some observations of distant galaxies[Wikipedia] and galaxy clusters[Wikipedia] show us the speed at which the stars and luminous gases contained in them move, while others show how much nearby galaxies focus the light moving past them from more distant galaxies; these observations and others thus tell us how massive these galaxies are. The total masses turn out to be many times greater than that of the luminous matter alone, meaning that almost all of the matter in the universe is invisible to us.

Even more surprising, very little of this dark matter appears to be the same sort of particles that make up the chemical elements in the things we’re familiar with. If the processes thought to have built those elements had produced enough to constitute all the dark matter, the relative proportions of each element should have come out quite different from what we actually see in the universe. So most of the dark matter is expected to be made of something entirely foreign to us. Many different possibilities are being examined through both astronomical observations and particle physics experiments, the possibilities representing different extensions of the known physical laws governing known types of matter.

Even relatively rare events that happen in only a tiny fraction of the possible opportunities can still be frequent if the opportunities occur often enough. Dark-matter particles seem to interact only rarely with ordinary matter, but where there’s enough ordinary matter (like a large object) for them to interact with, interactions might occur quite often. “High Energy Electron Signals from Dark Matter Annihilation in the Sun”[Information Bridge] makes the point that some of these results—namely the production of high-energy electrons—should be visible to us if dark matter does interact with ordinary solar matter in either of two particular ways.

The sun is not the only place to look for evidence of dark-matter interactions. The report “Dark matter searches with Cherenkov telescopes: nearby dwarf galaxies or local galaxy clusters?”[Information Bridge] addresses whether dwarf galaxies or galaxy clusters are the most promising objects to examine. The authors find that either will work better for different types of observational strategy, but that neither existing Cherenkov telescopes[Wikipedia] nor the planned Cherenkov Telescope Array[Information Bridge, Wikipedia] would be sensitive enough to detect the gamma rays that dark neutralinos[Wikipedia] ;would produce when they collided and annihilated each other.

The preceding experiments look for evidence of dark-matter interactions in outer space. But dark matter should also exist on earth, and other experiments look for dark-matter interactions here. The Cryogenic Dark Matter Search (CDMS) is an ongoing experiment of this type that looks for weak interactions[Wikipedia, Information Bridge] of dark matter with semiconductor nuclei. The reports “Phonon Quasidiffusion in Cryogenic Dark Matter Search Large Germanium Detectors”[Information Bridge] and “Monte Carlo Comparisons to a Cryogenic Dark Matter Search Detector with low Transition-Edge-Sensor Transition Temperature”[Information Bridge] describe the characteristics of semiconductors used to look for these interactions and how the semiconductors’ characteristics were found. Another report, “Search for inelastic dark matter with the CDMS II experiment”[Information Bridge], describes one way semiconductors have actually been used. Earlier results of the CDMS and other experiments indicate that galactic dark matter does interact with “ordinary” nuclei, but that the interacting particles’ total kinetic energy isn’t the same after the interaction. The CDMS II report mentions the discovery of three candidate dark-matter events; the probability that three or more such events under the same conditions do not involve dark matter is 11%.

The Cryogenic Dark Matter Search and other experiments of its type are conducted underground, so the earth shields the dark-matter detectors from most of the non-dark-matter cosmic rays that would produce similar reactions. Another underground experiment (“First Dark Matter Searches from a 4-kg CF3I Bubble Chamber Operated in a Deep Underground Site”[Information Bridge]), using a bubble chamber[Information Bridge, Wikipedia] to find evidence of dark-matter interactions with protons, determined a new upper limit on the probability of such interactions resulting in proton recoil.

While the preceding experiments involve waiting for existing dark-matter particles to interact with each other or something else and observing the result, other experiments attempt to produce dark-matter particles from the collisions of “ordinary” particles in high-energy accelerators. “Search for Low-Mass Dark-Sector Higgs Bosons”[Information Bridge] describes how evidence of a dark-matter analog of the Higgs boson has been sought from the end-products of electron-positron collisions at the SLAC National Accelerator Laboratory, while “Search for a dark matter candidate produced in association with a single top quark in collisions at = 1.96 TeV”[Information Bridge] and “A search for dark matter in events with one jet and missing transverse energy in collisions at = 1.96 TeV”[Information Bridge] describe similar searches for evidence of dark matter particles or particle-antiparticle pairs from the end-products of proton-antiproton collisions at Fermilab. (The “ = 1.96 TeV” in these titles means the energy of the collision[Wikipedia] is 1.96 trillion electron-volts[Wikipedia].) The interactions examined haven’t shown evidence of dark matter involvement, so they tell us something about what the dark matter isn’t. Such results are common in early investigations of new phenomena that there’s not much information about.

Strategies for future investigations of dark matter are described in other recent reports, each focusing on different assumptions about its nature. “Dark Matter Jets at the LHC”[Information Bridge] and “Dark Matter Particle Spectroscopy at the LHC: Generalizing MT2 to Asymmetric Event Topologies”[Information Bridge] each propose examining proton-antiproton experiments at Large Hadron Collider (LHC) at CERN (the European Organization for Nuclear Research). The former report considers whether dark matter undergoes strong interactions[Wikipedia] rather than just weak interactions as is commonly assumed, while the latter questions whether all dark matter particles produced in any given collision experiment are all of the same type, even in any one collision. “Singlet-Doublet Dark Matter”[Information Bridge] explores some general possible types of weakly-interacting matter to see how they might be detected in experiments and finds the prospects for demonstrating their existence or nonexistence in the near future “extremely promising”, while “Direct Detection of Sub-GeV Dark Matter”[Information Bridge] examines the possibility that dark-matter particles may be much less massive than most earlier investigations have supposed and considers how such low-mass particles’ effects on atoms might be detected.

Expansion of the universe and dark energy

Even accounting for dark matter, most of what affects the universe’s size isn’t matter or energy at all, at least in the usual sense.

While the smallness of Einstein’s constant makes it insignificant in regions of space as small as a planet, a solar system, or even a galaxy, it turns out to be very significant when considering gravity’s effect on the universe as a whole. The largest known features in the universe, intergalactic voids[Wikipedia], are a few hundred million light-years across—much larger than a galaxy, but a small fraction of the space that’s visible through telescopes. On this much grander scale of billions of light-years, the universe looks rather uniform, with luminous matter spaced more or less evenly throughout. According to Einstein’s equation, space that contains a uniform distribution of low-speed, low-stress matter and energy willmost likely change its size all the time, since each particle of matter contributes enough to the spacetime curvature to reduce any divergence of the particles’ paths away from each other, so that every particle has some attraction to every other. The rate of expansion or contraction will itself almost always change, in a way that depends on how densely packed with matter and energy the universe is (reflected by Tmn ), and on the size of the constant . The only way space would not expand or contract at all is if Tmn and had a very specific ratio; if the ratio were even slightly different, expansion or contraction would inevitably occur.

Distribution of local galaxies along particular directions from earth as mapped by the Sloan Digital Sky Survey. Points in color represent locations of galaxies; black spaces (other than the large empty wedges on the left and right sides, where the sky wasn’t mapped) show where no galaxies were found. These intergalactic voids, the largest structures found, are a few yottameters (a few hundreds of millions of light-years) wide, so any volume of space tens or hundreds of yottameters wide looks much like any other. On that scale the density of matter in the universe can be considered approximately uniform. (Image from Sloan Digital Sky Survey, http://www.sdss3.org/images/gallery/sdss_pie2.jpg)

Observations of more and more distant galaxies during the last century indicated that the universe is indeed getting bigger, its galaxies generally moving farther and farther apart. For most of the time since the first of these observations were made, it was generally expected that the combined effect of matter on the spacetime containing it would be to slow down the expansion of space. But late last century, observations made to determine exactly how much the expansion was decelerating indicated that the expansion was actually accelerating—an impossibility according to Einstein’s equation, unless were larger than a certain value. This can be seen more easily if the equation is algebraically rearranged as follows:

If (or ’ ) were negative or zero, the effect of an ordinary matter distribution Tmn on the curvature of spacetime would be to decelerate the expansion of space over time. But if ’ were greater than zero, then once the universe expanded enough to make the matter distribution Tmn less than ’gmn, the expansion’s acceleration would change from negative to positive, meaning the expansion would proceed faster and faster indefinitely.

The roles of both Tmn and gmn in determining Gmn, and thus how quickly the universe grows or shrinks, are similar enough that the term ’gmn can be treated as representing a peculiar sort of energy—one with anegative pressure exactly the same size as the energy density (in a -1:1 pressure-density ratio). Ordinary positive pressure, like the air pressure in a tire, has two opposing effects: an outward inflating force, and a gravitational attraction. On the other hand, negative pressure would exert an inward deflating force and a gravitational repulsion. So if any form of energy exerted a negative pressure throughout the entire universe, its gravitational repulsion would accelerate the universe’s expansion, even if the pressure were not in an exact -1:1 ratio with the energy’s density. For this reason the cause of acceleration is often referred to as dark energy—“dark” because it’s invisible, much like the dark matter responsible for the smaller-scale motions within galaxies and galactic clusters, and “energy” because (like light or other forms of energy) its pressure is at least roughly as large as its density, whereas the pressure of ordinary matter is much less than its density.

“Improved Dark Energy Constraints from ~ 100 New CfA Supernova Type Ia Light Curves”[Information Bridge] describes how more than doubling the amount of astronomical data about the acceleration of the universe’s expansion leads to a more precise determination of the pressure-density ratio of any dark energy. The late 20th-century observations that indicated the universe’s expansion is accelerating involved supernovae[R&D Accomplishments], whose distances and speeds are easier to determine than those of other celestial objects. TThe luminosities of stars that explode into type Ia supernovae[Wikipedia] are correlated with how quickly their luminosities rise and fall. From the rate of brightening and dimming, we can roughly determine their total light output, and from that information we can work out how far away they are by how much of their light we actually receive on earth (since stars of a given absolute brightness look dimmer, the further away they are). However, other factors besides a type Ia’s rate of brightening and dimming correlate to a lesser extent with their total light output. Observing more type Ia supernovae allows astronomers to determine these correlations more accurately and refine their estimates of supernova distances. The larger data set implies a narrower range of dark-energy pressure-density ratios that still encompasses the value -1:1.

Supernova observations are not the only possible means of determining the dark-energy pressure-density ratio. Three complementary sets of observations will also be gathered in the Dark Energy Survey: counts of galaxy clusters, oscillations of baryons, and weak gravitational lensing. “Status of the Dark Energy Survey Camera (DECam) Project”[Information Bridge] describes the camera built for use with the CTIO Blanco 4-m telescope[Wikipedia] to make this survey.

Evidence for dark energy is also being sought by laboratory experiments with atom waves, as indicated by the title of “A terrestrial search for dark contents of the vacuum, such as dark energy, using atom interferometry”.[Information Bridge] Water waves, sound waves, light waves, and other sorts of waves have a common feature. Whenever two sets of waves of the same kind cross paths, as wave peaks from the two sets occupy the same place, the peaks reinforce each other to make a bigger peak; likewise, bigger wave troughs are made when wave troughs from each set meet. On the other hand, when a peak from one wave meets a trough from the other, the two waves will interfere at that point and form only a small peak or trough there, if any. Even material objects have wave characteristics, but these tend to be most obvious when the objects are small, like molecules or atoms. The report describes how the interference of atom waves will be observed to check for the presence of any kind of dark energy that meets two criteria: density that varies from place to place, and a nongravitational effect on matter that has at least a certain minimum strength. Dark energy of this type should cause a measurable variation in the interference of atom waves as the atom interferometer moves through space.

References

The following books provide background on points not otherwise specifically referenced throughout this report regarding relativity theory and its cosmological implications.

Einstein’s Telescope: The Hunt for Dark Matter and Dark Energy in the Universe by Evalyn Gates (W. W. Norton & Company 2009). Thorough introduction to the evidence that the universe consists mainly of dark components. The “telescope” mentioned in the title refers to astronomers’ use of stars, galaxies, and galaxy clusters as natural gravitational lenses that focus light from beyond themselves. This focusing reveals much not only about the light sources, but about the mass distribution of the lenses themselves.

God’s Equation: Einstein, Relativity, and the Expanding Universe by Amir D. Aczel (Four Walls Eight Windows 1999). History of Einstein’s general-relativity equation relating spacetime’s curvature to the matter and energy it contains, from Einstein’s formulation of it through early tests to discovery of its implications about the structure and development of the universe, including the recent evidence that the universe’s expansion is accelerating.

The Principle of Relativity by H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, with notes by A. Sommerfeld; translated by W. Perrett and G. B. Jeffery (Dover 1952). Contains a translation of Einstein’s paper “Cosmological Considerations on the General Theory of Relativity”, in which he introduced the version of his spacetime-curvature equation with the cosmological term gmn given above.

Prepared by Dr. William N. Watson, PhysicistDOE Office of Scientific and Technical Information

The galaxy distribution map shown above is from the SDSS-III (Sloan Digital Sky Survey III) website. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/.

SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

As originally posted, the paragraph above describing the report “Improved Dark Energy Constraints from ~ 100 New CfA Supernova Type Ia Light Curves” incorrectly indicated that that the new set of supernova data improved calculations of the universe’s expansion rate by reducing the effect of random galactic motions rather than the additional factors related to the rise, fall, and total light output of type Ia supernovae. The paragraph was corrected in March 2015.—wnw